Imagine the area immediately surrounding the point of contact as a resistance extending for several yards and the earth beyond that point as a solid conductor.

As you know, if you pass a current through a resistance, you get a voltage drop across it. I don't pretend that these figures are accurate or representative, but just for the sake of argument let's say that a line at about 20kV (e.g. one leg of a 33kV delta) touches the ground and winds up with a resistance to earth of 2000 ohms. That'll result in about 10 amps flowing to ground (assuming a solidly grounded neutral).

Now suppose that the resistance area around that ground connection extends to 20 yards. That will result in a voltage gradient over which the 20,000V is distributed. If the gradient were linear across that 20 yd. distance, then somebody standing with his feet 1 yard apart would experience a potential difference of (2000 ohms / 20 yd.) * 10A = 1000V. [Linked Image]

In practice you'll find that the voltage gradient is much steeper closer to the point of contact and tapers off rapidly at the outer edges.